Three Cubes each of Volume 64cm^3 are Joined end to end to Form a Cuboid. Find the total Surface Area of the Cuboid so Formed? - Maths

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Three cubes each of volume 64`"cm"^3` are joined end to end to form a cuboid. Find the total surface area of the cuboid so formed?









Finding Side of Cube from Volume,


Given,

Volume of 1 cube  = 64`"cm"^3`
⇒ `"Side"^3` =  64`"cm"^3`
⇒ `"a"^3` =  64`"cm"^3`
⇒ `"a"^3` =  `4^3`

Surface area of cuboid

length of cuboid = a + a + a = 4 + 4 + 4 = 12 cm
Breadth = a = 4 cm
Height = a = 4 cm

Hence,

`l` = 12 cm, `b` = 4 cm, `h` = 4 cm

Area of Cuboid = 2 (`lb + bh + hl`)

= 2 (12`\times`4 + 4`\times`4 + 4`\times`12)
= 2 (48 + 16 + 48)
= 2 (112)
= 2`\times`112
= 224

Hence, Area of Cuboid = 224 `"cm"^2`

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